World Football Elo Ratings

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The World Football Elo Ratings is a ranking system for men's national association football teams that is published by the website eloratings.net. It is based on the Elo rating system but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. The FIFA World Rankings -not based on the Elo method- is the official national teams rating system used by the international governing body of football and is therefore more prevalent.

The ratings consider all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.[1] Ratings for teams with fewer than 30 matches should be considered provisional.

The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method performed poorly.[2]

Top 100 ranking[edit]

The following table shows the top 100 teams in the World Football Elo Ratings on 30 November 2016, using data from the World Football Elo Ratings web site.[3]

Each national team's FIFA World Rankings are shown as they were in the latest release on 24 November 2016.[4]

AFC
CAF
CONCACAF
CONMEBOL
OFC
UEFA
No confederation

Highest average ratings since 1970[edit]

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[5][6][7] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 December 2016. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score.

Rank Country Avg Elo
1  Brazil 2017.9
2  Germany[a] 1988.4
3  Netherlands 1932.4
4  England 1929.2
5  Italy 1926.3
6  Spain 1919.5
7  Argentina 1912.3
8  France 1893.0
9  Russia[b] 1853.3
10  Czech Republic[c] 1836.7
11  Portugal 1827.7
12  Serbia[d] 1817.9
13  Sweden 1802.8
14  Mexico 1790.2
15  Romania 1789.8
16  Uruguay 1779.3
17  Belgium 1774.8
Rank Country Avg Elo
18  Poland 1773.7
19  Denmark 1771.7
20  Scotland 1744.2
21  Chile 1732.1
22  Paraguay 1729.2
23  Republic of Ireland 1729.1
24  Bulgaria 1709.9
25  Australia 1699.9
26   Switzerland 1699.4
27  Austria 1697.0
28  Colombia 1696.7
29  Hungary 1691.5
30  South Korea 1681.8
31  Iran 1673.6
32  Greece 1663.2
33  Wales 1661.8
34  Egypt 1660.9
Rank Country Avg Elo
35  Nigeria 1660.3
36  Peru 1647.8
37  Turkey 1647.3
38  Israel 1643.1
39  Norway 1642.8
40  Cameroon 1639.6
41  Morocco 1636.0
42  Ivory Coast 1630.9
43  United States 1619.7
44  Ghana 1616.0
45  Northern Ireland 1610.6
46  Iraq 1607.0
47  Costa Rica 1605.7
48  Japan 1604.3
49  Tunisia 1599.3
50  Ecuador 1599.2
51  China PR 1591.1

List of number one teams[edit]

The following is the list of nations who have achieved the number one position in the World Football Elo Ratings since 1872:

Ranking by days as leader[edit]

Nation days First Date as Leader Last Date as Leader
 England 13,177 30 November 1872 11 June 1988
 Brazil 8,334 12 June 1958 Current
 Argentina 7,449 16 June 1929 9 Nov 2016
 Scotland 6,215 4 March 1876 23 Oct 1926
 Germany [e] 4,361 25 July 1966 28 May 2016
 Spain 2,535 5 September 1920 11 October 2013
 Italy 2,259 7 June 1934 15 August 2006
 Uruguay 2,020 18 September 1920 31 October 1929
 Hungary 2,001 2 August 1952 11 June 1958
 France 1,868 12 September 1984 10 July 2007
 Soviet Union [f] 1,450 31 March 1963 24 June 1988
 Netherlands 965 1 June 1978 3 July 2014
 Denmark 105 25 June 1916 7 Oct 1916
 Austria 11 27 May 1934 6 June 1934
 Czech Republic [g] 9 25 May 1924 7 June 2005

Elo all-time records[edit]

All-time highest ratings[edit]

The following is a list of national football teams ranked by their highest Elo score ever reached. The team in each confederation that has achieved the highest rank is shown in color.

All-time highest ranking[edit]

The following is a list of national football teams ranked by their highest Elo ranking ever reached. Note that for the highest ranking/rating of a national football team the Elo ratings website ignores the ranking/rating before 30 matches have been played.

Averages by decade[edit]

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9).

Rank 1920s 1930s 1940s [p] 1950s 1960s
1 1908

 Uruguay

1972

 Argentina

2035

 Argentina

2022

 Argentina

1972

 Brazil

2 1875

 Scotland

1965

 Italy

2005

 Italy

2016

 Hungary

1945

 Soviet Union

3 1867

 Spain

1893

 Uruguay

1908

 England

1997

 Brazil

1933

 England

4 1845

 Argentina

1887

 England

1876

 Brazil

1927

 England

1930

 Hungary

5 1822

 Czechoslovakia

1880

 Austria

1870

 Scotland

1878

 West Germany

1922

 Argentina

6 1814

 England [q]

1869

 Scotland

1859

 Spain

1860

 Yugoslavia

1893

 West Germany

7 1805

 Denmark

1866

 Spain

1845

 Uruguay

1856

 Uruguay

1876

 Czechoslovakia

8 1781

 Hungary

1819

 Czechoslovakia

1838

 Germany

1833

 Austria

1856

 Italy

9 1769

 Brazil

1809

 Brazil

1830

 Hungary

1822

 Italy

1849

 Spain

10 1768

 Austria

1805

 Hungary

1813

 Austria

1812

 Spain

1841

 Uruguay

11 1728

 Netherlands

1769

 Costa Rica

1788

 Czechoslovakia

1807

 Scotland

1826

 Yugoslavia

12 1711

 Sweden

1760

 Germany

1782

 Mexico

1803

 Sweden

1808

 Scotland

13 1693

 Belgium

1686

 Denmark

1765

 Wales

1797

 Paraguay

1794

 Sweden

14 1686

 Italy

1681

 Sweden

1752

 Sweden

1757

 France

1785

 Mexico

15 1677

 Portugal

1681

 Wales

1715

 Paraguay

1729

 Czechoslovakia

1742

 Austria

Rank 1970s 1980s 1990s 2000s 2010s [r]
1 2067

 Brazil

1980

 Brazil

2007

 Brazil

2000

 Brazil

2054

 Spain

2 2046

 West Germany

1971

 West Germany

1998

 Germany

1991

 France

2048

 Germany

3 1955

 England

1953

 Soviet Union

1962

 Italy

1973

 Netherlands

2044

 Brazil

4 1936

 Italy

1937

 England

1940

 France

1965

 Argentina

2000

 Netherlands

5 1890

 Netherlands

1900

 Argentina

1929

 Netherlands

1960

 Spain

1983

 Argentina

6 1884

 Poland

1899

 Italy

1912

 Spain

1946

 Italy

1919

 England

7 1879

 East Germany

1895

 France

1911

 FR Yugoslavia[s]

1922

 England

1892

 Chile

8 1878

 Soviet Union

1890

 Netherlands

1910

 England

1897

 Germany

1885

 Portugal

9 1863

 Argentina

1854

 Spain

1882

 Denmark

1893

 Portugal

1885

 Uruguay

10 1858

 Spain

1839

 Poland

1871

 Argentina

1884

 Czech Republic

1872

 Italy

11 1846

 Czechoslovakia

1830

 Belgium

1852

 Czech Republic[t]

1844

 Denmark

1870

 France

12 1840

 Hungary

1829

 Czechoslovakia

1846

 Russia[u]

1843

 Croatia

1864

 Colombia

13 1837

 Yugoslavia

1829

 East Germany

1844

 Sweden

1825

 Mexico

1856

 Mexico

14 1818

 Scotland

1826

 Yugoslavia

1830

 Mexico

1812

 Sweden

1837

 Croatia

15 1811

 Portugal

1792

 Scotland

1829

 Croatia

1809

 Romania

1798

 Sweden

16 1798

 Belgium

1789

 Romania

1828

 Romania

1794

 United States

1793

 Russia

17 1783

 Romania

1788

 Denmark

1814

 Portugal

1793

 Republic of Ireland

1789

 Ecuador

18 1777

 Sweden

1785

 Uruguay

1791

 Republic of Ireland

1792

 Turkey

1775

 Switzerland

19 1772

 Austria

1782

 Austria

1788

 Colombia

1780

 Uruguay

1771

 Ivory Coast

20 1762

 France

1781

 Sweden Wales

1780

 Belgium Norway

1777

 Russia

1769

 Ukraine

Highest rated matches[edit]

A list of the 16 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).

Rank Combined
points
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 4247  Germany 2184  Argentina 2063 1 : 0 aet 2014-07-13 World Cup F Brazil Rio de Janeiro
 Germany 2204  Argentina 2043 2 : 4 2014-09-03 Friendly Germany Düsseldorf
3 4223  Netherlands 2106  Spain 2117 0 : 1 aet 2010-07-11 World Cup F South Africa Johannesburg
4 4203  Brazil 2102  Germany 2101 1 : 7 2014-07-08 World Cup SF Brazil Belo Horizonte
5 4201  West Germany 2009  Hungary 2192 3 : 2 1954-07-04 World Cup F Switzerland Bern
6 4197  Brazil 2066  Spain 2131 3 : 0 2013-06-30 Confederations Cup F Brazil Rio de Janeiro
7 4165  Netherlands 2056  Brazil 2109 2 : 1 2010-07-02 World Cup QF South Africa Port Elizabeth
8 4162  West Germany 2074  Brazil 2088 0 : 1 1973-06-16 Friendly West Germany Berlin
9 4156  Brazil 2062  Netherlands 2094 0 : 0 2011-06-04 Friendly Brazil Goiânia
10 4149  Hungary 2169  Uruguay 1980 4 : 2 1954-06-30 World Cup SF Switzerland Lausanne
11 4148  Hungary 2141  Brazil 2007 4 : 2 1954-06-27 World Cup QF Switzerland Bern
12 4139  Spain 2091  Germany 2048 1 : 0 2010-07-07 World Cup SF South Africa Durban
13 4138  Netherlands 2077  Argentina 2061 0 : 0 2014-07-09 World Cup SF Brazil São Paulo
14 4130  Brazil 2056  West Germany 2074 1 : 0 1982-03-21 Friendly Brazil Rio de Janeiro
15 4125  Germany 2047  Brazil 2078 1 : 2 1998-03-25 Friendly Germany Stuttgart
16 4124  Brazil 2025  West Germany 2099 1 : 1 1977-06-12 Friendly Brazil Rio de Janeiro
17 4121  West Germany 2084  Netherlands 2037 2 : 1 1974-07-07 World Cup F West Germany Munich
18 4116  West Germany 2096  Brazil 2020 0 : 1 1978-04-05 Friendly West Germany Hamburg
19 4115  Argentina 2099  Chile 2016 0 : 0 2016-06-26 Copa América F United States East Rutherford
20 4112  Brazil 2097  Italy 2015 4 : 1 1970-06-21 World Cup F Mexico Mexico City

Biggest upsets[edit]

A list of the matches with the biggest point exchange. Since the importance of the match, the goal differential and the perceived home team advantage are factored in the point exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating.[v]
The nations' points before the matches are given.

Rank Point
exchange
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 91  Sweden 1636  Belgium 1764 8 : 1 1924-05-29 Olympic Games France Paris
2 88  Italy 1761  Spain 1902 7 : 1 1928-06-04 Olympic Games Netherlands Amsterdam
3 84  Czechoslovakia 1816  Argentina 1963 6 : 1 1958-06-15 World Cup Sweden Helsingborg
4 83  Norway 1530  Great Britain 1953 3 : 1 1920-08-28 Olympic Games Belgium Antwerp
 Egypt * 1590  Hungary 1823 3 : 0 1924-05-29 Olympic Games France Paris
6 82  Brazil 2102  Germany 2101 1 : 7 2014-07-08 World Cup Brazil Belo Horizonte
7 81  Ghana 1601  Czech Republic 1982 2 : 0 2006-06-17 World Cup Germany Cologne
8 80  Fiji 1208  New Zealand 1521 4 : 0 1980-02-23 OFC Nations Cup New Caledonia Nouméa
 Trinidad and Tobago 1445  Mexico 1749 4 : 0 1973-12-14 CONCACAF Championship Haiti Port-au-Prince
10 79  Turkey 1453  China * 1604 4 : 0 1948-08-02 Olympic Games United Kingdom Walthamstow
11 78  Croatia 1877  Germany 2062 3 : 0 1998-07-04 World Cup France Lyon
 Khmer Republic 1228  Kuwait 1508 4 : 0 1972-05-14 Asian Cup Thailand Bangkok
 Paraguay 1600  Uruguay 1974 3 : 0 1929-11-01 Copa América Argentina Buenos Aires
14 77  Uruguay 1786  Brazil 2127 3 : 0 1959-12-12 Copa América Ecuador Guayaquil
15 76  Netherlands 1967  Spain 2091 5 : 1 2014-06-13 World Cup Brazil Salvador
 United States 1866  Mexico 1769 0 : 5 2009-07-26 CONCACAF Gold Cup United States East Rutherford
 Chile 1553  Uruguay 1885 3 : 0 1937-01-10 Copa América Argentina Buenos Aires
18 75  Venezuela 1318  Bolivia 1625 3 : 0 1967-01-28 Copa América Uruguay Montevideo
 Costa Rica 1684  Guatemala * 1469 1 : 4 1946-03-10 CCCF Championship Costa Rica San José
20 74  Chile 1771  Brazil 2002 4 : 0 1987-07-03 Copa América Argentina Córdoba
 Denmark 1720  Italy 1985 5 : 3 1948-08-05 Olympic Games United Kingdom London
 Germany 1849  Norway 1682 0 : 2 1936-08-07 Olympic Games Germany Berlin

*The national teams of Egypt, China and Guatemala had only played 3, 18, and 24 international matches before their respective upsets (China only yet against East Asian teams), and their Elo rating may still be partially determined by the starting rating they have been assigned (the points exchanges could be lower when these are adjusted).

History[edit]

The Elo system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.

Overview[edit]

The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.

The factors taken into consideration when calculating a team's new rating are:

  • The team's old rating
  • The considered weight of the tournament
  • The goal difference of the match
  • The result of the match
  • The expected result of the match

The different weights of competitions in descending order are:

These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional.

Basic calculation principles[edit]

The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.

The ratings change are based on the following formulae:

or

Where;

= The new team rating
= The old team rating
= Weight index regarding the tournament of the match
= A number from the index of goal differences
= The result of the match
= The expected result
= Points Change

The number of Points Change is rounded to the nearest integer before updating the team rating.

Status of match[edit]

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Tournament or Match type Index (K)
World Cup 60
Continental Championship and Intercontinental Tournaments 50
World Cup and Continental qualifiers and major tournaments 40
All other tournaments 30
Friendly Matches 20

Number of goals[edit]

The number of goals is taken into account by use of a goal difference index.

If the game is a draw or is won by one goal

If the game is won by two goals

If the game is won by three or more goals

  • Where N is the goal difference

Table of examples:

Goal Difference Coefficient of K (G)
0 1
+1 1
+2 1.5
+3 1.75
+4 1.875
+5 2
+6 2.125
+7 2.25
+8 2.375
+9 2.5
+10 2.625

Result of match[edit]

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss). This also holds when a game is won or lost on extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).

Expected result of match[edit]

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

where dr equals the difference in ratings (add 100 points for the home team). So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.

Examples[edit]

The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Before the tournament the three teams have the following point totals.

Team Points
A 630
B 500
C 480

Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

Example 1[edit]

Team A versus Team B (Team A stronger than Team B)

Team A Team B Team A Team B Team A Team B
Score 3 : 1 1 : 3 2 : 2
20 20 20 20 20 20
1.5 1.5 1.5 1.5 1 1
1 0 0 1 0.5 0.5
0.679 0.321 0.679 0.321 0.679 0.321
Total (P) +9.63 -9.63 -20.37 +20.37 -3.58 +3.58

Example 2[edit]

Team B versus Team C (both teams approximately the same strength)

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:

Team B Team C Team B Team C Team B Team C
Score 3 : 1 1 : 3 2 : 2
20 20 20 20 20 20
1.5 1.5 1.5 1.5 1 1
1 0 0 1 0.5 0.5
0.529 0.471 0.529 0.471 0.529 0.471
Total (P) +14.13 -14.13 -15.87 +15.87 -0.58 +0.58

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

See also[edit]

Notes[edit]

  1. ^ Representing West Germany from 1949 to 1990
  2. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
  3. ^ Combined record of the Czechoslovakian (1970-1992) and Czech national football teams (1993-present)
  4. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
  5. ^ Combined record of the Germany (1908-1950 & 1990-present) and West Germany (1950-1990) national football teams.
  6. ^ So far, only the Soviet Union national football team (1924-1992) has reached the #1 position, but any future efforts by the Russia national football team (1992-present) will be included.[8]
  7. ^ Combined record of the Czechoslovakian (1920–1993) and Czech (1994–present) national football teams.
  8. ^ as Soviet Union
  9. ^ as FR of Yugoslavia
  10. ^ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
  11. ^ as Soviet Union
  12. ^ as Czechoslovakia
  13. ^ as FR of Yugoslavia
  14. ^ a b The combined Ireland national football team was in 4th to 6th place from its first match in 1882 to 1902, in a period that only 4 to 6 teams were in the rankings
  15. ^ as Zaire
  16. ^ In the 1940s, most national teams did not play games until after the end of World War II, making comparison of countries for this decade weak. For example, Mexico did not play any matches between Feb 1938 and July 1947, so that the average over the decade mostly reflects the single Elo rating achieved in February 1938
  17. ^ Includes the record of the Great Britain Olympic football team until and the 1920 Olympics
  18. ^ up to 1 December 2016
  19. ^ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
  20. ^ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
  21. ^ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)
  22. ^ In those terms, most surprising may have been the 2:1 win of Luxembourg (Elo rating 1049) over Switzerland (ER 1730) in a World Cup qualification match in September 2008 (a 681 point difference). In another World Cup qualifier in October 2004 Liechtenstein (ER 1046) held the 810 points higher rated Portuguese team (ER 1856) to a 2:2 draw.

References[edit]

  1. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012. 
  2. ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
  3. ^ World Football Elo Ratings Eloratings.net. Retrieved: 2016-11-30.
  4. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 24 November 2016. Retrieved 2016-11-24. 
  5. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  6. ^ Arpad Elo, Chess Life, 1962.
  7. ^ About the Chessmetrics Rating System, by Jeff Sonas
  8. ^ "History of the Football Union of Russia". Rfs.ru. Retrieved 2016-06-04. 

External links[edit]